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Stuart, A. M.; Humphries, A. R.
This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the...

Gonzalez, Oscar; Stuart, Andrew M.
A concise account of various classic theories of fluids and solids, this book is for courses in continuum mechanics for graduate students and advanced undergraduates. Thoroughly class-tested in courses at Stanford University and the University of Warwick, it is suitable for both applied mathematicians and engineers. The only prerequisites are an introductory undergraduate knowledge of basic linear algebra and differential equations. Unlike most existing works at this level, this book covers both isothermal and thermal theories. The theories are derived in a unified manner from the fundamental balance laws of continuum mechanics. Intended both for classroom use and for self-study,...

Pavliotis, Grigorios A.; Stuart, Andrew M.
This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. The book begins by setting the theoretical foundations of the subject area, and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions.
The presentation of the material is particularly suited to the range of...

Law, Kody; Stuart, Andrew; Zygalakis, Konstantinos
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.
The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material...

The laser as a radiation source with temporal and spatial coherence has made a tremendous impact in the different fields of science. As a result, new and exciting research has been developing allover the world. Laser spectro­scopy shares a large fraction of this research, and in the last decade nu­merous books and monographs have been published on this subject. Most of these books and monographs contain the work done in the physics community. Very few books represent the advances made in laser chemistry, a field that is flourishing and whose future is indeed very exciting. It was felt that a...

Despite major advances in the observation and numerical simulation of the atmosphere, basic features of the Earth's climate remain poorly understood. Integrating the available data and computational resources to improve our understanding of the global circulation of the atmosphere remains a challenge. Theory must play a critical role in meeting this challenge. This book provides an authoritative summary of the state of the art on this front.
Bringing together sixteen of the field's leading experts to address those aspects of the global circulation of the atmosphere most relevant to climate, the book brings the reader up to date on the key...

Over the last four decades, robotic spacecraft have visited nearly every planet, from torrid Mercury to frigid Neptune. The data returned by these Pioneers, Mariners, Vikings, and Voyagers have revolutionized our understanding of the solar system. These achievements rank among the greatest accomplishments of the 20th century. Now, at the opening of the 21st, it is appropriate to ask, where do we go from here?
In 2001, NASA asked the National Academies to study the current state of solar system exploration in the United States and devise a set of scientific priorities for missions in the upcoming decade (2003-2013). After...

Preface: This volume contains contributions presented at the 1990 Topical Meeting on Ultrafast Phenomena. The meeting, held in Monterey, California, from May 14 to 17, was the seventh in a biennial series whose purpose is to provide a forum for discussion of the latest advances in ultrafast optics and their application to fundamental scientific and engineering studies. The 362 registered participants, including liS students, represented a wide range of scientific and engineering disciplines and came from 18 different countries. Their enthusiasm, the originality and quality of the papers that were presented, and the beautiful coastal setting combined to produce a...

Preface: Metalloproteins play essential critical functional roles in enzymatically catalyzing reactions difficult to achieve without metals, in signal transduction, and in storage and transport of proteins constituting over 1/3 of the proteome of living organisms. Recent breakthroughs in crystallography have provided insights into understanding their mechanisms, but challenges remain in identifying the particularly redox states of the metals and in the chemical mechanisms for the complex reactions they catalyze. With these advances in structural information, theory and computation are starting to play a more significant role, particularly in identifying the reaction mechanism. This volume summarizes some of the recent progresses...

Aschbacher, Michael
We extend results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular we determine the maximal subgroups of this form. We also determine the maximal overgroups of short root subgroups in finite classical groups, and the maximal overgroups in finite orthogonal groups of c-root subgroups.

Engerman, Stanley L.; Hoffman, Philip T.; Rosenthal, Jean-Laurent; Sokoloff, Kenneth L.
Preface:
This volume contains papers first presented at a conference, "In Data Veritas: Institutions and Growth in Economic History," held in honor of Lance Davis at the California Institute of Technology, November 6-8, 1998. In addition to the presenters, also attending , as formal or informal discussions, were Karen Clay, Robert Cull, Price Fishback, Albert Fishlow, Stephen Haber, John James, Shawn Kantor, Zorina Khan, Margaret Levenstein, Rebecca Menes, Clayne Pope, and John Wallis. The Introduction and the Afterword were written by the editors at a later date. We wish to thank Frank Smith from Cambridge University Press and the two anonymous...